Fractals & Computer Modeling


fractal-circle-limitFractals are geometric patterns that are repeated at ever smaller or larger scales to create irregular surfaces and shapes that cannot be represented by classical geometry. Fractals are used in the computer modeling of irregular structures and patterns found in nature.

Fractals are therefore unique art forms that use mathematical formulas to create art that has an infinite diversity of detail, color, form, or light. The formula used to create a particular image will determine how every pixel in that image is colored and formed. A typical fractal image has millions of pixels.

Fractals, which are complex images of extraordinary beauty can emerge from simple mathematical formulas and by selectively changing color algorithms and through the modification of the formulas, you can create unique images never seen before.

The discovery of fractals helped the defining of irregular shapes that could not previously be represented or defined by mathematics. It was possible to define mathematically to define shapes such as squares and triangles but not irregular shapes such as a coastline, tree outline, etc.
What is the unique thing about fractals? One very interesting aspect of fractals is that they are infinite. They are infinite in two separate ways, the micro level, and the macro level. Fractals extend to infinitely higher values of their co-ordinates from the center outwards in all directions. It is somewhat like starting at the center of the universe and moving out to try to find the end of the universe.

Fractals also have infinite detail that in theory you can magnify without limit to show an ever-increasing detail within the image. This is one of the key aspects of fractals whether relative to exploring them as a form of art or as found in nature.
One more distinguishing feature of fractals is the property of self-similarity; arbitrary regions of the fractal resemble the whole fractal. Just as DNA stores all information about all of us, the parent image is what contains all the information in a fractal.
Fractals in nature and art can vary from the chaotic to those with beautiful symmetry, from massively chaotic thunderhead clouds to a perfectly symmetrical snowflake. However, regardless of the level of chaos, symmetry, they are simply everywhere you look.
In conclusion, this article has been a discussion about fractals and their use in computer modeling. As shown in the article fractals are quite important since they help map out nature digitally. Fractals are the building blocks for such things as computer games and virtual reality software programs. Without them probably digital mapping of nature would be impossible.